I dont own the PS3 version.
I have no idea whats up with the controls,but I have no issues with the game using the 360 controller when I use the swing stick.
I dont have a clue what the menu screens look like when you pause the PS3 version,but have u gone into the controller settings? you might find some sorta option there to to disable something.
The 360 version you either can select classic and swing with the A button,but you have to press it pretty hard *sometimes it has a button delay

and you wont swing*
But classic is for pussies and I use the swing stick.The way you describe how to use the swing stick is the right way,I'm not sure why its not working.
Maybe it's a bluetooth controller issue *shrug*